Question 105
In acute $\triangle ABC$ with centroid $G$, $AB = 22$ and $AC = 19$. Let $E$ and $F$ be the feet of the altitudes from $B$ and $C$ to $AC$ and $AB$ respectively. Let $G'$ be the reflection of $G$ over $BC$. If $E$, $F$, $G$, and $G'$ lie on a circle, compute $BC$.